Defining parameters
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.f (of order \(2\) and degree \(1\)) |
Character conductor: | \(\operatorname{cond}(\chi)\) | \(=\) | \( 28 \) |
Character field: | \(\Q\) | ||
Newform subspaces: | \( 2 \) | ||
Sturm bound: | \(32\) | ||
Trace bound: | \(3\) | ||
Distinguishing \(T_p\): | \(3\) |
Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(112, [\chi])\).
Total | New | Old | |
---|---|---|---|
Modular forms | 22 | 4 | 18 |
Cusp forms | 10 | 4 | 6 |
Eisenstein series | 12 | 0 | 12 |
Trace form
Decomposition of \(S_{2}^{\mathrm{new}}(112, [\chi])\) into newform subspaces
Label | Dim | $A$ | Field | CM | Traces | $q$-expansion | |||
---|---|---|---|---|---|---|---|---|---|
$a_{2}$ | $a_{3}$ | $a_{5}$ | $a_{7}$ | ||||||
112.2.f.a | $2$ | $0.894$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(-4\) | \(0\) | \(4\) | \(q-2q^{3}-2\zeta_{6}q^{5}+(2-\zeta_{6})q^{7}+q^{9}+\cdots\) |
112.2.f.b | $2$ | $0.894$ | \(\Q(\sqrt{-3}) \) | None | \(0\) | \(4\) | \(0\) | \(-4\) | \(q+2q^{3}+2\zeta_{6}q^{5}+(-2-\zeta_{6})q^{7}+q^{9}+\cdots\) |
Decomposition of \(S_{2}^{\mathrm{old}}(112, [\chi])\) into lower level spaces
\( S_{2}^{\mathrm{old}}(112, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 3}\)